Rewrite (x+2)(x-4) in Standard Quadratic Form

To find the standard representation of the quadratic function given by $f(x) = (x+2)(x-4)$, we will expand the expression using the distributive property, commonly known as the FOIL method (First, Outer, Inner, Last):

• First: Multiply the first terms in each binomial: $x \cdot x = x^2$.
• Outer: Multiply the outer terms in the binomials: $x \cdot (-4) = -4x$.
• Inner: Multiply the inner terms: $2 \cdot x = 2x$.
• Last: Multiply the last terms in each binomial: $2 \cdot (-4) = -8$.

Now, let's combine these results:

The expression becomes $x^2 - 4x + 2x - 8$.

Next, we combine like terms:

The terms involving $x$ are $-4x + 2x$, which simplifies to $-2x$.

Thus, the expression simplifies to: $f(x) = x^2 - 2x - 8$

Upon comparing this result to the provided choices, we find that it matches choice 3.

Therefore, the standard representation of the function is $f(x) = x^2 - 2x - 8$.